Pavement Foundation Layers Phase I Principal Investigator: Bora - - PowerPoint PPT Presentation

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Environmental Impacts on The Performance of Pavement Foundation Layers – Phase I

Principal Investigator:​ Bora Cetin, Ph.D. Co-Principal Investigator: Tuncer Edil, Ph.D. Kristen Cetin, Ph.D. Research Team: Debrudra Mitra

May 20, 2020

Department of Civil and Environmental Engineering​ Michigan State University

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PROBLEM STATEMENT

IMPACTS OF FREEZE-THAW CYCLES UNDER ROADS ▪ Water in soil freezes and expands ▪ During spring-thaw, melted water and infiltrated water trapped above the zone of frozen subgrade – strength loss under heavy loading ▪ Seasonal Load Restrictions – applied to avoid/reduce damages ▪ Prediction of Freeze-Thaw Cycles – Monitoring systems & Computational Models

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INSTRUMENTATION

▪ Instrumented with an array of:

• Soil Moisture
• Temperature

▪ Weather Station to measure climate data

• On site

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OBJECTIVES

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Develop a Data Driven Model to Predict the Frozen Soil Depths & Freeze-Thaw Durations

• Inputs:
• Climate data (precipitation, relative humidity, percent sunshine,

temperature, & wind speed)

• Layer thicknesses
• Material type
• Output
• Number of freeze-thaw cycles at specific depths
• Duration of freezing and thawing
• Frost depth

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Overview of Research Plan

➢ Task 1 – Initial Memorandum on Expected Research Benefits and Potential Implementation Steps ➢ Task 2 – Field Data Collection ➢ Task 3 – Modelling Analyses ➢ Task 4 – Final Report

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TASK 2 – FIELD DATA COLLECTION

List of data that will be collected:

▪

Climate Data

• Air temperature
• Percent sunshine
• Precipitation
• Wind speed
• Relative humidity

▪

Soil Data

• Material data
• Temperature
• Water content

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Develop a tool that can be used to assess/predict the freeze- thaw behavior of roadways

• Simple
• Stand-alone
• For any location (where soil profile and weather data

are available) Output needed:

• number of freeze thaw cycles at certain depth
• frost depth isotherms over time

Modeling Objectives: Task 3 – Modelling Analyses

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Two types of modeling approaches to consider: Physics-based modeling (“white box”) Data-driven modeling (“black box”)

Modeling Approaches

What is the appropriate approach to consider?

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Different approaches towards modeling:

Physics-Based Modeling

based on physical principles and relationships between variables; described with a set of mathematical equations with variables that have physical meaning

Inputs: Many input (or assumptions) required; some may or may not be known Pros: better at extrapolation, limited historical data required Cons: significant knowledge of all physical properties and interactions; slower (higher computational intensity)

Data-Driven Modeling

Statistical or machine learning based; uses historical data to develop a quantifiable relationship between inputs and outputs

Inputs: whatever data is available (and ultimately found to be significant) Pros: lower computational intensity; no knowledge of physical properties or interactions required Cons: worst (typically) at extrapolation outside of bounds of original data; needs larger training dataset to create and validate

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Tool Development Process: Workflow

• 4. Evaluate performance for

different sets of data

• 6. Final tool

Yes No

• 1. Collect data
• 2. Data pre-processing and

QA/QC

• 3. Develop (new) data-

driven model(s)

• 5. Improve model

Desired accuracy reached?

Can the model be improved further?

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Most important requirements for data-driven modeling are:

• large(r) input datasets, which will be split into:
• In-sample (to create the model)
• out-of-sample (to validate the model)
• diversity of conditions (e.g. hot/cold, wet/dry,

etc..) Data needed (ideally):

▪ Weather data (close or near to site) ▪ Soil profiles/characteristics (thermal/moisture) ▪ Historical temperature at different depths ▪ A range of sites/locations of data collection

Step 1. Collect data: Data Needs

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QA/QC: Types & Handling of Missing Data:

1)

Short spans (less than 10 hrs)

→ Impute data (fill it in) based on trends in surrounding data → forward fill method 2)

Long spans (more than 10 hrs) in this dataset

→ Remove the time periods with missing data

Division of Data

Step 2. Data Pre-Processing:

Cleaned Dataset Training Data Test Data Used to create/train the model Used to evaluate the model performance

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Step 3. Develop data-driven models: Process

Layout of model development process

Historical weather data Soil profile Number of freeze thaw cycles at certain (input) depth Frost depth isotherms

• ver time

INPUT LAYER – Data input OUTPUT LAYER “BLACK BOX” Soil temp/ moisture data Depth of Interest Data-driven model

Training Data

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Step 3-6. Refine Model: Progressive Improvement

Stepwise/Regression models Neural network models Deep learning models Example (other models are considered) sequence from simple to complex modeling to determine relative improvement in performance

• 1. Start with simplistic

approach / model

• 2. Compare

predicted & actual temps. & F/T Use as final model

Yes No

• 3. Use same approach,

different method of data segregation

No Continue iteration

Accept- able result?

Yes

• 4. Update/

change model Acceptable result?

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Model Selection: (a) geotech literature review

Previous literature on data-driven models: Most to date have attempted to predict average daily or monthly soil temperatures, NOT hourly data, or freeze- thaw /isotherm information

• Regression [2,5]
• Artificial Neural Networks [3-5]
• Neuro-fuzzy inference system (ANFIS) [1, 6]
• Multilayer perceptron (MLP) [6]
• Generalize regression, radial basis, and MLP neural network

[7]

• Support Vector Machine (SVM) [8]

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Model selection: (b) general literature review

Literature on modeling multi-variate time series data Our approach: Simple → complex

• Regression
• Linear & non-linear
• Stepwise
• Vector autoregressive (VAR)
• multivariate time series analysis
• Vector error correction model (VECM)
• can be useful when there are cointegrated variables
• ANN, MLP, SVM, ANFIS (also in prev. slide)
• Many others…

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(1,3) (2)

Order of Evaluation / Presentation Discussion

(4)

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Soil temperature correlation with climate parameters

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Closest to surface (T1) Farthest from surface (T12)

Temperature is strongest predictor

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▪ Soil temperature is significantly corelated with air temperature ▪ Correlation coefficient reduces with the depth of soil ▪ Wind is negatively correlated with soil temperature ▪ RH is very weakly correlated with soil temperatures

Soil temperature correlation with climate parameters

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▪ Initially, a simple model has been selected, and then

sequentially proceed towards the complex models.

▪ (a) Linear regression model (all variables) ▪ (b) Stepwise regression to evaluate the significant input

variables.

(1) Regression Models: Methods

Soil temperature Regression coefficients Regression intercept Air Temp Rain RH Wind TC_1 1.04 0.19

• 0.07
• 0.59

12.13 TC_2 1.02 0.18

• 0.05
• 0.69

10.51 TC_3 0.92 0.02 0.05

• 0.86

4.49 TC_4 0.84 0.02 0.08

• 0.77

2.42 TC_5 0.83 0.03 0.09

• 0.75

2.38 TC_6 0.81 0.06 0.09

• 0.72

2.37 TC_7 0.80 0.07 0.09

• 0.71

2.41 TC_8 0.76 0.12 0.09

• 0.66

2.59 TC_9 0.66 0.14 0.04

• 0.41

4.93 TC_10 0.60 0.11 0.09

• 0.54

2.88 TC_11 0.39 0.08 0.10

• 0.40

5.49 TC_12 0.47 0.04 0.09

• 0.41

3.44

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▪ Training Data: first 50,000 datapoints ▪ Testing Data: remaining 9,522 datapoints The error for all temperature values are shown below for both datasets (note all weather variables used as predictors)

(1) Regression Models: Data division

Training Data Test Data (not used to develop the model)

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All weather data input were considered; only those variables found to have *significant* influence are provided below, in

• rder of most to least; Air temperature is most important

(1) Regression Models: Stepwise

Temperature node Significant inputs TC_1 Air temperature, Relative humidity, Wind speed, Precipitation TC_2 Air temperature, Relative humidity, Wind speed, Precipitation TC_3 Air temperature, Relative humidity, Wind speed TC_4 Air temperature, Relative humidity, Wind speed TC_5 Air temperature, Relative humidity, Wind speed TC_6 Air temperature, Relative humidity, Wind speed TC_7 Air temperature, Relative humidity, Wind speed TC_8 Air temperature, Relative humidity, Wind speed TC_9 Air temperature, Relative humidity, Wind speed TC_10 Air temperature, Relative humidity, Wind speed TC_11 Air temperature, Relative humidity, Wind speed TC_12 Air temperature, Relative humidity, Wind speed

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(1) Regression Models: Performance summary

▪ Linear regression and polynomial regression models are used as the starting point ▪ Simplistic model ▪ Polynomial regression performs better compared to linear regression ▪ Overall, there is some amount of error in temperature prediction that can likely be improved

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(Using weather variables only as predictors)

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(1 → 3) Regression Models: Additional considerations

Soil temperature pattern varying depending on several parameters:

▪ Seasonal patterns ▪ Daily patterns ▪ Depth ▪ Soil characteristics

Next we tried (2) several non-regression methods, then returned to (3) an improved regression method

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(2) Vector Models: Summary

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(a) Vector Auto Regressive (VAR) (b) Vector Error Correction Model (VECM) (c) Vector Auto Regressive Moving Average (VARMA)

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Data:

▪ Training Data: first 45,000 datapoints (memory limitations)

Aug/2017 – Nov/2018

▪ Testing Data: remaining 9,522 datapoints

Model:

▪ Forecast length: 10 days ▪ Maximum lag criteria: 24; selected based on Bayesian information criterion (BIC) ▪ First order differencing used to remove stationarity of data

(2) Vector Models: Data division & details

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(2) Vector Models: Results Summary

▪ Unable to capture hourly or daily fluctuations but can capture seasonal variations ▪ VECM and VARMA > VAR Not the best approach for our needs

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(1 → 3) Regression Models: Additional considerations

Soil temperature pattern varying depending on several parameters:

▪ Seasonal/Daily patterns ▪ Depth ▪ Soil characteristics

3 new variables considered:

▪ Day of year (1-365); ▪ Timestep (1 – 4 step/hour X 24 hours) per day ▪ Hours (1 – 24 hours/day X 365 days); (i.e. 15 min = 0.25)

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(3) Regression Models: Updated Methods

▪ Forward Stepwise regression: select the most important parameters

• Selected variables are: Day of Year, Timestep, Air

Temperature, RH, Wind speed, Rain

▪ Consider: ▪ Linear and Non-linear (completed in R) ▪ Polynomial regression (power of 2, 3, 4)

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▪ Training Data: first 35,040 datapoints (1 year)

Aug/2017 – Aug/2018

▪ Testing Data: remaining 10,270 datapoints (23% of

data)

(3) Regression Models: Data division

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(3) Regression Models: Results Summary

▪ Non-linear regression (NLR) of 4th order performs best ▪ Error reduces with increasing depth ▪ RSE (below) and R-squared (next slide) used for evaluation

1 2 3 4 5 T1 T2 T3 T4 T5 T6 T7 T8 T10 T12

RSE values

Poly4 Poly3 Poly2 Linear

1 2 3 4 5 T1 T2 T3 T4 T5 T6 T7 T8 T10 T12

RSE values

Poly4 Poly3 Poly2 Linear

Training data Testing data

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(3) Regression Models: Results Summary

Adjusted R2 values are higher than 0.95 for all surfaces

0.7 0.75 0.8 0.85 0.9 0.95 1 T1 T2 T3 T4 T5 T6 T7 T8 T10 T12

Adjusted R2 values

Poly4 Poly3 Poly2 Linear 0.7 0.75 0.8 0.85 0.9 0.95 1 T1 T2 T3 T4 T5 T6 T7 T8 T10 T12

Adjusted R2 values

Poly4 Poly3 Poly2 Linear

Training data Testing data

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(3) Regression Models: Error by Depth

Training Data

• 30
• 20
• 10

10 20 30 T1

• 30
• 20
• 10

10 20 30 T5

• 30
• 20
• 10

10 20 30 T7

• 30
• 20
• 10

10 20 30 T10

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(3) Regression Models: Error by Depth

Testing Data

• 30
• 20
• 10

10 20 30 T1

• 30
• 20
• 10

10 20 30 T3

• 30
• 20
• 10

10 20 30 T5

• 30
• 20
• 10

10 20 30 T7

• 30
• 20
• 10

10 20 30 T10

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(3) Regression Models: Summary & Next Steps

For (3):

• Polynomial regression performs better compared to
• ther methods
• The results of (3) are better than (1) and (2)

Next Steps:

▪ Neural network ▪ Multi-layer perceptron model, ▪ Support Vector Machine, ▪ Neuro-fuzzy inference system, ▪ Deep learning algorithms

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By predicting temperature our ultimate goal is to predict the # of freeze-thaw (F-T) cycles

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Calculation of Freeze-Thaw Cycles: Questions

Key Questions: (1) How do we define (calculate) a freeze- thaw cycle from soil data? (2) How accurate are the data we are using?

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• Weather and soil temperature: measured at 15

minutes time intervals

• Temperature accuracy: +/- 1 C

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0∘C Freezing point thaw freeze Soil temperature

Calculation of Freeze-Thaw Cycles: Method

Assumed 0 C (for now) What should this width be?

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Method Used (for now, focus on flexibility in code)

• 1. Temperature above 0 ∘C => Liquid (thaw)
• 2. Temperature below freezing point => Solid (freeze)
• 3. Temperature within freezing point and 0 ∘C

=> phase transformation state

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Calculation of Freeze-Thaw Cycles: Method

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Freezing temperature considered (9 total):

• 0.001 ∘C (i.e. no temp difference)
• 0.1 ∘C
• 0.2 ∘C
• 0.25 ∘C
• 0.3 ∘C
• 0.4 ∘C
• 0.5 ∘C
• 0.75 ∘C
• 1 ∘C

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Calculation of Freeze-Thaw Cycles: Method

Sensor Depth (in) TC_1 3 TC_2 4 TC_3 9.5 TC_4 15 TC_5 16 TC_6 18.5 TC_7 19.5 TC_8 24 TC_9 36 TC_10 48 TC_11 60 TC_12 72

Shallow Mid Deep

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Datasets: 2017 ( July-Dec), 2018 ( Jan-Dec), 2019 (Jan-Apr)

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20 40 60 80 100 120 140 160 180 T1 T2 T3 T4 T5 T6 T7 T8 T10 T12

For 2017 data (July-Dec : Start of winter)

0.001 0.1 0.2 0.25 0.3 0.4 0.5 0.75 1

Calculation of Freeze-Thaw Cycles: Results

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Datasets: 2017 ( July-Dec), 2018 ( Jan-Dec), 2019 (Jan-Apr)

Advanced Testing and Characterization of Iowa Soils and Geomaterials 40

Calculation of Freeze-Thaw Cycles: Results

100 200 300 400 500 T1 T2 T3 T4 T5 T6 T7 T8 T10 T12

For 2018 data (Jan-Dec : 1 whole year)

50 100 150 200 250 300 T1 T2 T3 T4 T5 T6 T7 T8 T10 T12

For 2019 data (Jan-Apr : End of winter)

0.001 0.1 0.2 0.25 0.3 0.4 0.5 0.75 1

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# of F-T: dependent on freezing point temperature

• Shallow soils (0-15 in): more F-T cycles that deep

soils;

• Mid-level soils (16-24 in) (min annual temp. ~ -1 to -

2∘C): # of F-T significantly influenced by F-T algorithm tolerance since more fluctuations near 0 ∘C range

• Deep soils (36-72 in) : # of F-T ~0 / generally does

not go below 0 ∘C or change states

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Calculation of Freeze-Thaw Cycles: Summary

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# of F-T: if we choose a tolerance of 1 C

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Calculation of Freeze-Thaw Cycles: Summary

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# of F-T: if we choose a tolerance of 1 C If we consider multiple locations (Note: sensors T3-T7 in different

locations are at different depths thus cannot be easily compared)

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Calculation of Freeze-Thaw Cycles: Summary

* Thermocouple error

cell 186 cell 188 cell 189 cell 127 cell 728 T1 3 56 58 66 71 44 T2 4 28 30 27 64 35 T3 6.5-9.5 1 1 2 11 4 T4 9-15 1 1 1 3 1 T5 10-16 1 1 1 2 1 T6 12-18.5 2 1 1 2 1 T7 18-19.5 2 1 1 2 1 T8 24 3 1 1 2 1 T9 36 30* 1 1 2 1 T10 48 1 T11 60 T12 72 2017 September to 2018 August Sept 2017 - August 2018 Soil surfaces Depth (in)

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# of F-T: if we choose a tolerance of 1 C If we consider multiple locations (Note: sensors T3-T7 in different

locations are at different depths thus cannot be easily compared)

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Calculation of Freeze-Thaw Cycles: Summary

cell 186 cell 188 cell 189 cell 127 cell 728 3 35 50 44 49 28 4 10 22 17 39 17 6.5-9.5 3 2 3 7 4 9-15 2 1 1 3 4 10-16 2 2 1 4 5 12-18.5 1 1 1 2 1 18-19.5 1 1 1 1 1 24 1 1 1 1 1 36 1 1 1 1 1 48 1

• 1

60 72 Sept 2018 to August 2019 Depth (in)

Review other larger tolerances above 1 C Compare soil profiles at locations (potential impact

• f F-T variations)

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▪ Compare data of different locations to find the freezing temperature at different locations ▪ Compare actual and predicted freeze-thaw cycles

• btained from the regression analysis

▪ Implement and test the performance of different complex models (ANN, Multi-layer perceptron model, Support Vector Machine, Neuro-fuzzy inference system, Deep learning algorithms)

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Next Steps: